Abstract:
Gaussian processes (GPs) provide a gold standard for performance in online settings, such as sample-efficient control and black box optimization, where we need to update a posterior distribution as we acquire data in a sequential online setting. However, updating a GP posterior to accommodate even a single new observation after having observed n points incurs at least \mathcal{O}(n) computations in the exact setting. We show how to use structured kernel interpolation to efficiently reuse computations for constant-time \mathcal{O}(1) online updates with respect to the number of points n, while retaining exact inference. We demonstrate the promise of our approach in a range of online regression and classification settings, Bayesian optimization, and active sampling to reduce error in malaria incidence forecasting.
